Inheritance in hierarchical relational structures

A brief survey is conducted of the inheritance principle the conveyance of properties between components within a hierarchical relational structure. The standard form of inheritance is considered, using the subset (is-a) relation and highlighted as an example of downward inheritance. Downward inheritance is extended to specialisation of actions, and cases are presented in which the rule fails. sider them on tile same plane of generality and abstractness as the standard hierarchical inheritance rules. Upward inheritance, on the other hand, is formally on the same plane as the more common downward form. Our analysis shows that the explanation for this powerful tool resides in one semantical aspect of a large class of very common relations. 2. D o w n w a r d inheri tance An alternative and less well-known form of inheritance is introduced upward inheritance. Several examples in which upward inheritance is valid and others in which it is not valid are given, in a treatment highlighting the analogy with downward inheritance. The validity of the rule, in those case in which it operates, is underlined, to distinguish it from induction. A brief acconnt is given of tile search for the underlying reasons for the validity of inheritance rules and these are then given. The solution turns out to be due to a hidden or implicit quantifier within the relations that are used. The semantical nature of the problem and of its solution are stressed, emphasising the impossibility of a purely syntactic analysis and solution to the problem. Various points of interest arising from the analysis ,are listed and discussed.